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%% Copyright (C) 2008 Alexander Barth
%%
%% This program is free software; you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation; either version 2 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; If not, see <http://www.gnu.org/licenses/>.
% Example program of the optimal interpolation toolbox
% the grid onto which the observations are interpolated
[xi,yi] = ndgrid(linspace(0,1,100));
% background estimate or first guess
xb = 10 + xi;
% number of observations to interpolate
on = 200;
% create randomly located observations within
% the square [0 1] x [0 1]
x = rand(1,on);
y = rand(1,on);
% the underlying function to interpolate
yo = 10 + x + sin(6*x) .* cos(6*y);
% the error variance of the observations divided by the error
% variance of the background field
var = 0.1 * ones(on,1);
% the correlation length in x and y direction
lenx = 0.1;
leny = 0.1;
% number of influential observations
m = 30;
% subtract the first guess from the observations
% (DON'T FORGET THIS - THIS IS VERY IMPORTANT)
Hxb = interp2(xi(:,1),yi(1,:),xb',x,y);
f = yo - Hxb;
% run the optimal interpolation
% fi is the interpolated field and vari is its error variance
[fi,vari] = optiminterp2(x,y,f,var,lenx,leny,m,xi,yi);
% Add the first guess back
xa = fi + xb;
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